I decided exact diagonalizing would be the smartest thing to do for a start. In concept, calculating the entanglement entropy from the ground state of a exact diagonalization procedure is fairly straightforward. Conceptualizing and writing the algorithm for diagonalizing a one diimensional Fermionic Hubbard chain has been fun. I shall only mention the trick that makes the whole process really elegant and fun. Any site has four possibilities namely no fermions, only spin-up, only spin-down and both spins. The four possibilities are very neatly cataloged with binary 00,01,10 and 11. So we take a binary string twice as long as the number of sites and every two bits of it represents the occupation of a site. Then we only have to count through the numbers from all 0's to all 1's and all the possible bases of the Hamiltonian are enumerated. I wish that was all the challenge there was. Unfortunately, it looks like I am looking at a long list of woes which starts with limited computer resources. Turns out, exact diagonalizing takes an unbelievably long time. My desktop has not finished a diagonalization of 10 sites in 6+ days, so far. I want to focus on bench-marking the answers first, to make sure the code works right. I shall post again when that is done.

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